Chapter 10, Problem 27CR

To determine

To construct: the triangle $\Delta RST$ .

Explanation of Solution

Given information:

The given line segment is as follows:

  

  $RS=a,RT=c$

Median of $\overline{RS}$ length b

Procedure to construct$\Delta RST$:

• Draw the line $RS=a$.
• Draw the perpendicular bisector of $RS$ , that intersect the line $RS$ at point D.
• As D as center with length b draw an arc and as R as center with length c draw an arc intersecting previous arc. Label as T.
• Join the lines $RT$and $ST$.
• Then required triangle $RST$ is formed.

The construction is shown below.

  

Hence, the triangle $\Delta RST$ is constructed.